On n-isoclinic Groups

Isoclinic Classification of Some Pairs $(G,G\')$ of $p$-Groups

‎‎The equivalence relation isoclinism partitions the class of all pairs of groups‎ ‎into families‎. ‎In this paper‎, ‎a complete classification of the set of all pairs $(G,G')$ is established‏‎,‎ whenever‎ $G$ is a $p$-group of order at most $p^5‎‏$‎ and ‎$p$ is a prime number greater than 3. Moreover‎, ‎the classification of pairs $(H,H')$ for extra special $p$-groups $H$ is also given.

n-cyclicizer groups

on $n$-kappe groups

let $g$ be an infinite group and $nin {3‎, ‎6}cup{2^k| kin mathbb{n}}$‎. ‎in this paper‎, ‎we prove that $g$ is an $n$-kappe group if and only if for any two infinite subsets $x$ and $y$ of $g$‎, ‎there exist $xin x$ and $yin y$ such that $[x^n‎, ‎y‎, ‎y]=1$‎.

Some properties of n-capable and n-perfect groups

In this article we introduce the notion of n-capable groups. It is shown that every group G admits a uniquely determined subgroup (〖Z^n)〗^* (G) which is a characteristic subgroup and lies in the n-centre subgroup of the group G. This is the smallest subgroup of G whose factor group is n-capable. Moreover, some properties of n-central extension will be studied.

Limit groups and groups acting freely on R n-trees.

We give a simple proof of the finite presentation of Sela's limit groups by using free actions on R n-trees. We first prove that Sela's limit groups do have a free action on an R n-tree. We then prove that a finitely generated group having a free action on an R n-tree can be obtained from free abelian groups and surface groups by a finite sequence of free products and amalgamations over cyclic ...